1. Field of the Invention
The present invention relates to a method of producing a microwave dielectric for use in a very high frequency (300 MHz.about.30 GHz) filter, a voltage-controlled oscillator, a global positioning system antenna, etc. More particularly, the present invention relates to a method of producing a microwave dielectric which can achieve temperature compensation for the applied circuities by controlling the temperature coefficient of the microwave dielectric such as a paraelectric.
2. Description of the Prior Art
A microwave dielectric including TiO.sub.2 was first developed by Richtmyer in 1939. However, it has not been in practical use since TiO.sub.2 has a high temperature coefficient (.apprxeq.450 ppm/.degree. C.) of the resonant frequency. Accordingly, there have been efforts to improve its characteristics by developing its new compositions and manufacturing processes. For instance, Zr of ZrTiO.sub.4 system was replaced by Sn to stabilize its irregular high-temperature phase even at a normal temperature and to arrange its temperature coefficient to reach almost Zero. [Elsevier Applied Science, Electronic Ceramics, pp. 76-78 (1991)]. Meanwhile, the temperature coefficient of a microwave dielectric was controlled by forming secondary phases having a polarity opposite to that of primary phases by using additives or substitution agents (i.e., if the temperature coefficient of the primary phases is positive, that of the secondary phases will be negative). [Japanese Journal of Applied Physics, Vol. 30, No. 913, pp. 2350-53 (September, 1991); Electronic Ceramics, Vol. 24, No. 124, pp. 4-10 (September, 1993); Journal of American Ceramic Society, 73[6], pp. 1599-605; Journal of American Ceramic Society, 67[4], pp. 1499-605 (1984)].
Generally, the wavelength .lambda..sub.d of the standard wave of a microwave dielectric is almost the same as its diameter. In other words, .lambda..sub.d .apprxeq.D. The resonance frequency f.sub.o of a dielectric is given by ##EQU1## where C=velocity of light in free space, and .lambda..sub.0 =wavelength of light in free space. The velocity V.sub.d and the wavelength .lambda..sub.d in a non-magnetic dielectric are given by ##EQU2## where .epsilon..sub.r =dielectric constant. Thus, ##EQU3##
If the temperature changes, .epsilon..sub.r and D also change, causing f.sub.o to change. The following expression is obtained by differentiating the expression (1) with respect to the temperature T: ##EQU4## where ##EQU5## Thus, EQU TC.sub.j =-(1/2TC.sub..epsilon.e +.alpha..sub.L) (3)
[Chapman and Hall, Electroceramics, pp. 230-241 (1990)].
If we assume that a sintered body is composed of phases of an i system, the following expression is given by a logarithmic mixture rule, ##EQU6## where k=relative dielectric constant, V.sub.i =volume fraction of phase i, and k.sub.i =relative dielectric constant of phase i. Differentiating the above expression, we get ##EQU7## Substituting the equation (3) for TC.sub..epsilon., we get ##EQU8## [Journal of American Ceramic Society, 73[6], pp. 1599-605 (1990)] from the resultant expression, it appears that the temperature coefficient of the resonance frequency of the dielectric is calculated by summing the temperature coefficient of the resonance frequency of each secondary phase. Accordingly, the entire temperature coefficient can be adjusted by properly mixing the phases having a positive or negative temperature coefficient different from each other, i.e., by properly adjusting the composition rate of the phases.
However, the conventional method of controlling the temperature coefficient of a dielectric as described above has the drawback in that additives or substitution agents should be put in the primary phases in order to create the secondary phases, thereby deteriorating other dielectric characteristics except the temperature coefficient.